A method of this kind is described in the international application PCT/DK95/00430. In this previous method, the stapling plungers as well as the associated clamping members were adapted to move in directions substantially parallel to the passage, in which the graft vessel was placed in readiness for establishing an end-to-side anastomosis with e.g. a coronary artery. With such an arrangement, the number of staples as well as their mutual closeness were limited by the purely mechanical need for guiding the stapling plungers in their operative movement, with the result that in the "seam" connecting the two vessels, there could be substantial distances between adjacent staples.